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Answer :
To solve the equation [tex]\(15x^2 + 13x = 0\)[/tex] using the quadratic formula, we start by identifying it as a quadratic equation in the standard form [tex]\(ax^2 + bx + c = 0\)[/tex].
For the given equation:
- [tex]\(a = 15\)[/tex]
- [tex]\(b = 13\)[/tex]
- [tex]\(c = 0\)[/tex]
The quadratic formula is given by:
[tex]\[
x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{2a}
\][/tex]
Now, let's plug in the values:
1. Calculate the Discriminant:
[tex]\[
b^2 - 4ac = 13^2 - 4 \times 15 \times 0 = 169 - 0 = 169
\][/tex]
2. Find the Square Root of the Discriminant:
[tex]\[
\sqrt{169} = 13
\][/tex]
3. Use the Quadratic Formula to Find Solutions:
- First solution:
[tex]\[
x_1 = \frac{{-13 + 13}}{2 \times 15} = \frac{0}{30} = 0
\][/tex]
- Second solution:
[tex]\[
x_2 = \frac{{-13 - 13}}{2 \times 15} = \frac{-26}{30} = -\frac{13}{15}
\][/tex]
Thus, the solutions for the equation [tex]\(15x^2 + 13x = 0\)[/tex] are [tex]\(x = 0\)[/tex] and [tex]\(x = -\frac{13}{15}\)[/tex].
Therefore, the correct answer is:
a. [tex]\(x = -\frac{13}{15}, 0\)[/tex]
For the given equation:
- [tex]\(a = 15\)[/tex]
- [tex]\(b = 13\)[/tex]
- [tex]\(c = 0\)[/tex]
The quadratic formula is given by:
[tex]\[
x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{2a}
\][/tex]
Now, let's plug in the values:
1. Calculate the Discriminant:
[tex]\[
b^2 - 4ac = 13^2 - 4 \times 15 \times 0 = 169 - 0 = 169
\][/tex]
2. Find the Square Root of the Discriminant:
[tex]\[
\sqrt{169} = 13
\][/tex]
3. Use the Quadratic Formula to Find Solutions:
- First solution:
[tex]\[
x_1 = \frac{{-13 + 13}}{2 \times 15} = \frac{0}{30} = 0
\][/tex]
- Second solution:
[tex]\[
x_2 = \frac{{-13 - 13}}{2 \times 15} = \frac{-26}{30} = -\frac{13}{15}
\][/tex]
Thus, the solutions for the equation [tex]\(15x^2 + 13x = 0\)[/tex] are [tex]\(x = 0\)[/tex] and [tex]\(x = -\frac{13}{15}\)[/tex].
Therefore, the correct answer is:
a. [tex]\(x = -\frac{13}{15}, 0\)[/tex]
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